FRA discounting

CFA Level I Derivatives
#1

Ex. An FRA settles in 30 days. It is based on a notional principal amount of $1million. 90-day LIBOR. Specifies a forward rate of 5%.

Assume that actual 90-day LIBOR 30-days from now is 6%. Compute cash settlement at expiration…

Now, the answer could have been payment from short to long of:-

(6%-5%)(90/360) * $1m = $2500.

However, since $2500 in savings would not come until the end of the 90-day loan period, the value at settlement is the present value of savings?? Discounting this at 6% (and not 5%) returns the present value at the settlement date. So the answer is $2500 * (1 + 6%*90/360) = $2463.05

Questions:

  1. Because the settlement is being made after the stipulated period of 30 days, why is discounting needed? Is the payment being made after 30 days or 90 days??

Fine, if the payment is being made after 90 days since the rate is unknown on the 30th day, and known only after the end of the 90-day period, the period of 90 days is from the inception of the contract. In which case, after settlement date only 90-30 = 60 days are left. So the discounting for the payment to be made on the settlement date should occur using 60 and not 90… which means the payment is $2475.248 $2500 * (1+6%*60/360)

  1. And if discounting of 90 days has been used, then does not it mean that the payment is getting made today?

So, is the short making the payment

today, or,

after 30 days?, or,

after 90 days?, or,

after 90 days after 30 days? or

after 60 days after 30 days?

  1. Can there be an FRA such as - 180 day FRA on a 90-day LIBOR? In that case what about the discounting?
#2

Ok I think I have found some more info on this. Goes like this–

a 30 day FRA based on 90-day LIBOR. This means that after 30 days, they will see what a 90-day LIBOR is. Based on this rate, the 2 parties would settle the transaction. So, after the end of the 30-day period, say the 90-day LIBOR is 6%. So, the short would pay the long this difference (or savings) after 90 days after the date of settlement. In a way, settlement means that the rate would be decided only. Payment should be made after 90 days.

Because he is making the payment on the settlement day, and not after 90 days, so, discounting using 90 days happens!!

Phew! Seems valid?

#3

I wrote an article on FRAs that may be of some help here: http://financialexamhelp123.com/fras/.

The opening paragraph says it all: the FRA is essentially and agreement to enter into two 90-day loans starting 30 days from today. If you actually entered into the loans, they’d be settled 120 days from today (at the end of the loan period). The FRA is settled 30 days from today, at the (then) PV of the 90-day settlement.